A fundamental and unsolved problem in speech processing is that of enhancing and separating speech signals from complicated and noisy mixtures, a problem also known as the coctail party problem. It isan extremely important problem as most state-of-the-art speech processing systems operate under the assumption that only one, clean source is present. This project aims at exploring fundamentally new ways of solving this problem by generalizing novel theoretical results in optimal temporal filtering methods that have recently been introduced by the applicant to multiple microphones, resulting in so-called spatio-temporal filtering methods. The filters are optimal in that they let the signal of interest pass undistorted while everything else is attenuated as much as possible. These methods may hold the key to solving the aforementioned problem as they, unlike state-of-the-art methods, do not require that the statistics of the noise and interfering speech signals are known, something that is especially important when dealing with non-stationary noise.